An optimal matching problem

Ekeland, Ivar

doi:10.1051/cocv:2004034

Ekeland, Ivar

ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 57-71.

Résumé

Given two measured spaces $(X, μ)$ and $(Y, ν)$ , and a third space $Z$ , given two functions $u (x, z)$ and $v (x, z)$ , we study the problem of finding two maps $s : X \to Z$ and $t : Y \to Z$ such that the images $s (μ)$ and $t (ν)$ coincide, and the integral $\int_{X} u (x, s (x)) d μ - \int_{Y} v (y, t (y)) d ν$ is maximal. We give condition on $u$ and $v$ for which there is a unique solution.

MR Zbl | 2 citations dans Numdam

DOI : 10.1051/cocv:2004034

Classification : 05C38, 15A15, 05A15, 15A18
Mots-clés : optimal transportation, measure-preserving maps

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Ekeland, Ivar. An optimal matching problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 57-71. doi : 10.1051/cocv:2004034. https://www.numdam.org/articles/10.1051/cocv:2004034/

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